Problems such as centroid and centroid in postgraduate mathematics
We say that when the "geometry" is regarded as a "material body" with uniform mass distribution, then the "centroid" of this material body is the "centroid" of the corresponding geometry. So, on the surface, "centroid" and "centroid" are two different concepts. One is aimed at "geometry", which is only related to the shape of geometry. The other is aimed at "material body", which is not only related to shape, but more importantly to density. But from the mathematical model, there is no essential difference between "centroid" and "centroid". The so-called "center of mass" concept is actually the "center of gravity" of the past, just a new norm. In the past, objects were calculated by volume and weight (kg), so they were called specific gravity, center of gravity and static moment related to center of gravity. Now the name of "volume" remains unchanged, while "weight" is always standardized as "mass" (kilogram), so other corresponding names have long been renamed as "density", "center of mass" and "mass moment". It is wrong to say that the "center of gravity" is related to the weight of the object! According to the past, it should be considered that the "center of gravity" is related to the different "specific gravity" (function) of an object at different points. "Weight" is a general concept, and "specific gravity" is a partial concept. It can be clearly said that the "center of gravity" of an object has nothing to do with its weight. It is also wrong to say that the center of mass is related to matter. Will "steel blocks" and "cement blocks" with the same density distribution have different centers of mass because of different substances?